Prédiction des états d'equilibre d'un champ thermique en turbulence homogène

Abstract

The aim of this work is to compare the prediction of several second order models in a thermal field of two cases of homogeneous turbulence. The second order models retained for this work are the classic models of Launder, Reece and Rodi [J. Fluid Mech. 68 (1975) 537–576], and the elaborate one of Launder et al. [Accomodating the effects of high strain rates in the modeling the pressure strain correlation, 1987, The University of Manchester of Science and Technology, March T.F.D/87/5/; A model for the pressure scalar gradient correlation and its application to homogeneous and inhomogeneous shear flow, Turbulent Shear Flow 7, Stanford University, USA, 1989, pp. 12-1–12-6; M. Hallback, D.S. Hennigson, A.V. Johansson, P.H. Alfredsson (Eds.), Turbulence Transition Modelling, Dordrecht, 1996] and Lumley and Shih [Second order modeling of passive scalar turbulent flow, Ph.D. Thesis, Cornell University, New York, 1984; Second order modeling of scalar in turbulent shear flow, in: Center of Turbulent Research 27th Aerospace Meeting, January 9–12, Nevada, 1989; M. Hallback, D.S. Hennigson, A.V. Johansson, P.H. Alfredsson (Eds.), Turbulence Transition Modeling, Dordrecht, 1996]. The main objective is the prediction of the equilibrium states of dimensionless parameters characterizing the two homogeneous flows considered. This comparison is referred to the experimental results of Sirivat and Warhaft [J. Fluid Mech. 128 (1983) 323–345] and the Large eddy simulations of Chasnov [Phys. Fluids 6 (2) (1994) 1036–1051] in the case of the decaying of homogeneous turbulence, to the experimental results of Tavoularis and Corrsin [J. Fluid Mech. 104 (1981) 311–347], and the numerical simulation of Rogers et al. [J. Fluid Mech. 203 (1989) 77–101] in the case of homogeneous sheared turbulence submitted to a thermal field. A Runge–Kutta method is used for the integration of the modeled differential equations and has shown that the elaborate models of Launder et al. [Accomodating the effects of high strain rates in the modeling the pressure strain correlation 1987, The University of Manchester of Science and Technology, March T.F.D/87/5/; A model for the pressure scalar gradient correlation and its application to homogeneous and inhomogeneous shear flow, Turbulent Shear Flow 7, Stanford University, USA, 1989, pp. 12-1–12-6; M. Hallback, D.S. Hennigson, A.V. Johansson, P.H. Alfredsson (Eds.), Turbulence Transition Modelling, Dordrecht, 1996] ensure the best approximation of the equilibrium states observed experimentally and from the direct numerical simulation.